Determine the amplitude and period of the function without graphing. Show your work.
y = 7/3cos (-2π/3x)
The general form of the function is y = A*cos(Bx), where A is the amplitude and B is the coefficient of x.
In this case, the amplitude, A, is equal to 7/3 because it is the coefficient in front of the cosine function.
The period, P, is defined as the distance it takes for the cosine function to complete one full cycle. The period can be found using the formula P = 2π/|B|, where B is the coefficient of x.
In our function, B = -2π/3. Therefore, the period P is equal to 2π/|-2π/3| = 2π/(2π/3) = 3.
So, the amplitude of the function is 7/3 and the period is 3.